Asynchronous time-interleaved waveform generator using harmonic mixing

ABSTRACT

Waveforms generators include a splitter that splits a digital input signal into a number of split signals each having a split signal frequency bandwidth that is substantially similar to a digital input signal frequency bandwidth. The split signals are mixed with associated digital, harmonic signals to generate a number of digital, mixed signals, which are then converted to analog signals at an effective sample rate that is different from a first order harmonic signal of at least one of the digital, harmonic mixers. A number of analog, harmonic mixers mix the associated analog signals with associated analog, harmonic signals to generate mixed, analog signals. The mixed, analog signals are combined into an output signal having an output signal bandwidth that is greater than a bandwidth of at least one of the number of DACs.

CROSS REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional PatentApplication No. 61/803,970, filed Mar. 21, 2013, which is incorporatedherein in its entirety.

FIELD OF THE INVENTION

This disclosure relates to waveform generators and methods of generatingwaveforms. More specifically, this disclosure relates to high speedarbitrary waveform or function generators using harmonic mixing.

BACKGROUND

Usable bandwidths of waveform generators, such as Arbitrary WaveformGenerators (AWGs) or Arbitrary Function Generators (AFGs), can belimited by a digital to analog converter (DAC) that is used to generatethe signal from a digital waveform sequence. The usable bandwidth of aDAC is limited by the lesser of the analog bandwidth or one half themaximum sample rate of the DAC. Conventional techniques for generatinghigher bandwidth output signals with existing DAC limitations can becomplex and expensive systems.

For example, synchronous time interleaving can be used to achieve aneffective higher DAC sample rate. Multiple DACs generate waveforms froma split input sequence that is offset in time within a single DAC sampleperiod. The analog signals are combined for a sample rate that iseffectively multiplied. However, in the examples in which the analogbandwidth of the DACs becomes the limiting factor, a high bandwidthactive combiner, such as an analog multiplexer or sample and holdmultiplexer, is needed to achieve the higher bandwidth.

Conventional multiplexed time interleaved systems cause the multiplexerto be clocked at a sample rate similar to the DAC channel bandwidth sothat the DAC has sufficient time to transition and settle during themultiplexer clock interval. The DACs are synchronously clocked to themultiplexer, in these conventional systems, so that each DAC sample isgated and then selected by the multiplexer. Such a limitation of the DACbandwidth limits the DAC sample rate and, in turn, limits themultiplexer clock rate. As a result, these conventional systems needmany DAC channels to achieve the desired performance.

As the number of DAC channels increases, the overall cost and complexityof the system correspondingly increases. For instance, each DAC requiresa separate memory and digital input path, as well as clocking and amethod of synchronizing all DAC channels, which requires a physicallylarge and complex multiplexing chip. The increased size and complexityof the multiplexing chip also results in longer communication paths, andtherefore, an increase in parasitic capacitance, inductance,electromagnetic noise, and design difficulties, among other challenges.

In another technique, sub-bands of an input signal are digitallydownconverted to a frequency range that can be passed through a lowersample rate DAC. The large input signal bandwidth is split into multiplelow bandwidth DAC channels. After being converted to analog signals atthe low bandwidth of the DACs, the sub-bands are digitally upconvertedto the respective original frequency ranges and combined into arepresentation of the digital input signal. However, when converting anarbitrary input signal having a frequency content that is routed througha single DAC channel, the recombined output contains inherent noisebecause it has signal energy from only one DAC channel and a noiseenergy from all DAC channels, which degrades the overall signal-to-noise(SNR) ratio of the system.

Accordingly, the art would benefit from waveform generating devices andmethods having an improved SNR.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an example waveform generator that usesharmonic mixing, according to embodiments of the invention.

FIG. 2 is a block diagram of another example waveform generator thatuses harmonic mixing, according to embodiments.

FIGS. 3A, 3B, 4A, 4B, 5A, 5B, and 6 are example spectral components ofvarious signals generated by the example waveform generator shown inFIG. 1.

FIGS. 7A, 7B, 8, 9, and 10 are circuit diagrams of example harmonicmixers of the disclosed waveform generators.

DETAILED DESCRIPTION

This disclosure describes embodiments of a DAC system for waveformgenerators that increases the sample rate and usable bandwidth of theanalog output signal by using harmonic mixing.

FIG. 1 is a block diagram of an example waveform generator 100 that usesharmonic mixing and, various filters, some of which may be optional invarious examples. The waveform generator 100 includes a splitter 102that is structured to receive a digital input signal 104. The splitter102 is structured to split the digital input signal 104 into a pluralityof split signals 106. The digital input signal 104 can be any suitablewaveform data sequence.

Each of the split signals 106 has a split signal frequency bandwidththat is substantially similar to the input signal frequency bandwidth.The splitter 102 can be any variety of circuitry that can split thedigital input signal 104 into multiple signals. For example, the splitsignals 106 can include any desired digital input stream having a givensample rate and includes recorded, stored, and/or generated datasequences.

The split signals 106 are input to digital, harmonic mixers 108 that arestructured to digitally mix its associated split signal 106 with anassociated digital, harmonic signal to generate a digital, mixed signal110. Each of the digital, harmonic mixers produces a digital, mixedsignal. The digital harmonic signal can include a local oscillator (LO)112 that applies the harmonic signals to the split signals, as shown inFIG. 1. The digital LO can be a numerically-controlled oscillator, insome example systems.

The digital, harmonic mixers 108 are any device that is configured tomix a signal with multiple harmonics. Although multiplication and/ormixing has been described in connection with harmonic mixing, as will bedescribed in greater detail below, any device that has the effect ofmultiplying a signal with multiple harmonics can be used as a harmonicmixer.

In some examples, the multiple harmonics can include a zero-orderharmonic, or a DC component. For example, the harmonic signal can be asignal represented by equation (1):

harmonic signal=1+2*cos(2π*F ₁ *t)   (1)

In equation (1), F₁ represents the first-order harmonic and t representstime. Thus, a signal having the form of equation (1) has harmonics at DCand at frequency F₁.

An inverted phase signal harmonic can be a signal represented byequation (2):

inverted harmonic signal=1−2*cos(2π*F ₁ *t)   (2)

Similar to the harmonic signal represented by equation (1), the invertedharmonic signal has harmonics at DC and frequency F₁. However, thefirst-order harmonic at frequency F₁ is out of phase by 180 degreesrelative to the similar first-order harmonic in the harmonic signalrepresented by equation (1).

Referring again to FIG. 1, the mixed, digital signals 110 are input tofilters 114. The mixed, digital signals 110 can have a sample rate thatis greater than the maximum effective sample rate of the DACs 122 andcan include a frequency bandwidth that is greater than one half theeffective sample rate of the DACs 122. The filter 114 can limit thebandwidth of the mixed, digital signals to prevent aliasing signaldistortion. The filter can include a symmetric Low Pass Filter (LPF)that generates a net filtering of the mixed signals that has a frequencyresponse that is substantially complementary to about one half of afrequency of the first-order harmonic of the harmonic signals. Thefrequency response at a given offset higher than F₁/2 and the frequencyresponse at a given offset lower than frequency F₁/2 can add to one.Although one has been used as an example, other values can be used asdesired, such as for scaling of signals. Further, the above example isdescribed as an ideal case. The implemented filtering can have adifferent response to account for non-ideal components, calibration, andthe like.

The symmetric filter is shown in the digital domain 116 of the waveformgenerator shown in FIG. 1, but can, additionally or alternatively, beincluded in the analog domain 118 in other examples. The filtered, mixeddigital signals 120 are input to associated Digital to Analog Converters122 (DACs). The sample rate of the filtered, mixed digital signals 120is downsampled to match the sample rate of the DACs, which can becombined with the filters 114, in some examples. The downsampling canoccur by decimating the output sequence of the filtered, mixed digitalsignals 120, such as by keeping a fewer number of samples of the outputsequence.

Any of the above-described splitting, filtering, mixing, and/ordownsampling can be implemented by any suitable digital circuitryincluding, but not limited to, a digital signal processor (DSP), amicroprocessor, a programmable logic device, general purpose processor,or other processing system with appropriate peripheral devices, asdesired, including complete integration to fully discrete components.

Each of the DACs 122 are structured to convert the filtered, mixed,digital signals 120 into analog signals 124. The DACs 122 are anyvariety of circuitry that is configured to convert a digital signal toan analog signal. Each DAC 122 can include an amplifier, filter,attenuator, and other digital or analog circuitry, as needed, toamplify, filter, attenuate or otherwise process the signal before orafter the digital signal is converted to an analog signal.

The DACs 122 are configured to operate at an effective sample rate. Inthe example waveform generator shown in FIG. 1, DACs 122 are shown as asingle DAC, but in other examples each DAC may include multiple,interleaved DACs operating at a lower sample rate to achieve a highereffective sample rate.

The effective sample rate of the DAC 122 (or the multiple, interleavedDACs) is different from a first order harmonic signal of at least one ofthe associated digital harmonic mixers 108. A first-order harmonic of atleast one of the digital, harmonic signals is different from aneffective sample rate of at least one of the DACs 122. For example, thefirst-order harmonic F₁ of the harmonic signal could be 20 GHz and asample rate of the DAC 122 could be 25 GS/s. Thus, the first-orderharmonic F₁ is different from the effective sample rate of the DAC 122.

In some examples, the first-order harmonic of a digital, harmonic signalneed not be an integer multiple or sub-multiple of the effective samplerate of the DACs 122. The first-order harmonic of a harmonic signal thatis associated with the digital, harmonic mixers 108 is not an integermultiple or sub-multiple of the effective sample rate of the DACs 122.

In some examples, the first-order harmonic of a harmonic signal can bebetween the effective sample rate of the DAC 122 and one half of theeffective sample rate of the DAC 122. Such a frequency of thefirst-order harmonic allows for higher frequency components above and/orbelow the first-order harmonic to be downconverted in frequency to bebelow one half of the sample rate of the DAC 122. Thus, such frequencycomponents can be effectively converted to an analog signal 124 by DACs122. Each of the bands of the split input signal goes through all paths.When more than one channel is combined for processing a single inputsignal, each channel or path receives substantially the entire bandwidthof the digital input signal. As the digital input signal is transmittedthrough all of the DACs, the SNR is improved.

The analog signals 124 are input to optional filters, such as thereconstruction filters 126 shown in the example waveform generator 100of FIG. 1. The reconstruction filters 126 are structured to filter theanalog signals 124 from the DACs 122 and substantially eliminate the DACimage frequency components in signals 124. The reconstruction filterscould be part of the DACs and/or the mixers, in some alternativeexamples.

The filtered analog signals 128 are input to a number of associatedharmonic, analog mixers 130. There is one mixer 130 for each of thesplit signal channels. The harmonic, analog mixers 130 are structured tomix an associated one of the filtered, analog signals 128 with ananalog, harmonic signal to generate a number of mixed, analog signals134.

In some examples, the analog, harmonic signals are substantially similarin frequency and phase to the corresponding digital, harmonic signals.The harmonic, analog mixers' harmonic signal can include a localoscillator (LO) 132 that applies the harmonic signals to the filteredanalog signal 128. The LO 132 of the analog, harmonic signal can besynchronized with the LO 112 of the digital harmonic signal, asdescribed in greater detail below.

The scaling factors for the digital, harmonic signals and the analog,harmonic signals can be the same or similar to each other even thoughthey are respectively digital and analog signals. The output signalsfrom the analog, harmonic mixers are referred to as remixed signals 134.

The remixed signals 134 are input to a single combiner 136 that isstructured to combine the number of remixed (or mixed), analog signals134 into an output signal 138 having an output signal bandwidth that isgreater than a bandwidth of at least one of the number of digital toanalog converters. The analog, output signal 138 from the combiner 136is a reconstruction of the digital input signal 104 that is applied tothe splitter 102.

Some form of synchronization of the harmonic signals 112, 132 is used.For example, the harmonics of the analog harmonic signals can be lockedto a clock related to the DAC. A frequency of the digital and analogmixers can be a harmonic of a lower-speed clock that is present in theDAC channels in the analog form, but is also correlated to the digitaldata stream. In other examples, the digital harmonic signal or relatedsignal is also converted by a DAC and is available in the analog domainto synchronize with the analog, LO signal. In still another example,out-of-band tones can be added to one or more of the mixed, digitalsignals. Using a first-order harmonic of 20 GHz, 11.25 GHz, or 9/16 of20 GHz, can be added to the mixed, digital signal. Since the added tonescan be set to be outside of the bandwidth that is established by theoptional digital filter(s), approximately 9 GHz depending on thetransition band, the tones can have a substantially negligible effect onthe reconstructed signal that is output from the combiner. The tones,however, can be less than a Nyquist frequency, i.e., less than 12.5 GHzfor a 25 GS/s sample rate, which means that the tones can be acquired byusing the analog, mixed signal before it is filtered. Regardless of thesynchronization technique used, a phase and frequency relationshipbetween the digital, harmonic signals and the analog, harmonic signalsis maintained.

FIG. 2 is an example of a waveform generator 200 having an input signal202 that is split by a splitter 204 into two DAC channels 206, 208. Theexample shown in FIG. 2 includes specific, example values for variouscomponents and for the signal frequency, sample rates, etc. The digitalinput signal 202 is an arbitrary waveform sequence having a sample rateof 50 GS/s. The digital input signal 202 is band-limited to 18 GHz toprevent mixing components from the various harmonic signals fromextending past adjacent harmonic frequencies. The sequence is replicatedand each path is interpolated to 2× the sample rate of the digital inputsignal or 100 GS/s by the splitter 204.

The replicated signal is then digitally mixed by digital mixers 210, 211with the zero'th and first harmonics of a 20.3125 GHz clock 212, 213,using an inverted (180 degree phase-shifted) clock between the two paths206, 208. The mixed, digital signals 214 are then symmetrically low passfiltered 216 and decimated to a sample rate of 25 GS/s, which is thesample rate at the input of each associated DAC 218. The digitalharmonic mixing and the filtering step can be combined with a decimatingfilter, if desired. The DAC outputs are again filtered with areconstruction filter 220 to remove the image signal produced by the DACitself and to have a net response from the analog mixer output that issymmetric in amplitude around a frequency of 10.15625 GHz (i.e., halfthe harmonic signal bandwidth).

The filtered, analog signals 222 are then mixed by an analog mixer 224in the analog domain with the same zero'th and first harmonics of the20.3125 GHz digital clock 212, again using an inverted (180 degreephase-shifted) clock between the two paths. The two paths are summed atthe combiner and filtered to remove content above 20.3125 GHz.

In the example arbitrary waveform generator 200 shown in FIG. 2, the LOs212, 213 of the digital, harmonic mixers 210, 211 and the LO 226 of theanalog, harmonic mixers 224 can use the 13^(th) harmonic of a dividedsample clock. (25 GHz/16=1.5625 GHz, 13*1.5625=20.3125 GHz).

FIGS. 3A-6 are examples of spectral components of various signals in thewaveform generator system shown in FIG. 2. FIG. 3A shows spectrum 300 asa spectrum of the digital input signal and hence, the split signal ofFIG. 2. Using the above example of the harmonic signal defined inequation (1), a DC component of the harmonic mixer passes the splitsignal, as represented by spectrum 300. However, the spectrum 300 in theinput signal is also mixed with the first-order harmonic at frequencyF₁. The resulting spectrum 302 is the product of such mixing. Thus, thedigital mixed signal includes components of spectrum 300 and spectrum302. Here, and in other figures, the spectral components are illustratedas separate and overlapping, however, the actual spectrum would be thecombination of the spectra 300 and 302.

Referring to FIG. 3B, spectrum 310 similarly represents components ofthe inverted digital mixed signal due to the mixing of the digital inputsignal with the DC harmonic of the inverted LO signal of the digitalharmonic mixer. The spectrum 312 similarly represents the mixed productof the inverted LO and the spectrum 310. As described above, thefirst-order harmonic of the inverted LO signal of the digital harmonicmixer is phase shifted by 180 degrees from the first-order harmonic ofLO signal 212. The 180 degree phase shift in the inverted digitalharmonic signal induces a 180 degree phase shift in the spectrum 312.The 180 degree phase difference is illustrated as a dashed line in FIG.3B.

FIGS. 4A and 4B represent the spectrums of the filtered digital mixedsignals. Filtering can occur, in this example, in the digital and/oranalog domain of the disclosed waveform generator systems and methods.For example, the digital mixed signals could be filtered with a digitalsymmetric LPF having a cutoff frequency near one half of the effectivesample rate of the DACs. In some examples, the filtering can be afunction of inherent filtering of the corresponding DACs, the digitalfilters, or the like.

In some examples, the net filtering of the digital mixed signals canresult in a frequency response that is substantially complementary toabout one half of a frequency of the first-order harmonic of the LOsignals of the digital mixers. The frequency response at a given offsetthat is higher than frequency F₁/2 and the frequency response at a givenoffset lower than frequency F₁/2 can add to one. Although one is used inthis example, other values can be used, as desired, such as for scalingof signals. Further, the above example is described as an ideal case andadditional filtering can be used to account for non-ideal components,calibration, etc. In an example system, a decimation filter, symmetricfilter, and calibration filter are also used to compensate for non-idealresponses in the analog domain.

In a particular example of the frequency response, using the 20.3125 GHzF₁ described above, frequency F₁/2 is 10.15625 GHz. From DC to 9.12625GHz, the frequency response is one. From 9.15265-11.15625 GHz, thefrequency response linearly changes from one to zero, passing through ½at 10.15625 GHz. The resulting spectral components are shown in FIGS. 4Aand 4B. FIG. 4A shows the filtered, mixed analog signal that includes alower frequency portion of the spectrum 200, illustrated by 400, and alower frequency portion of spectrum 302, illustrated by spectrum 402.Due to the digital mixing, spectrum 402 includes frequency components ofa higher sub-band of spectrum 300, albeit reversed in frequency.Similarly, the spectral components 410 and 412 of FIG. 4B correspond tothe lower frequency components of spectra 310 and 312 of FIG. 3A. The180 degree phase relationship of spectrum 312 is preserved in spectrum412.

Accordingly, through the harmonic mixing, two sub-bands of the digitalinput signal are converted to analog signals even though the span of thesub-bands would have exceeded a Nyquist bandwidth associated with theDACs. Each mixed signal, whether analog, digital, filtered, or the like,includes components of each sub-band of the digital input signal, suchas a low frequency sub-band and a high frequency sub-band of thespectrum 300 shown in FIGS. 4A and 4B.

For example, the sub-bands of the digital input signal are frequencyshifted to be within a bandwidth of a baseband sub-band. In someexamples, each sub-band of the digital input signal is frequency shiftedto be within the bandwidth of the single sub-band. However, depending onthe number of sub-bands, and the harmonic signals, each sub-band may notbe present in each mixed signal.

FIGS. 5A and 5B represent the spectra of the remixed signals that areinput to the combiner. As described above, the analog, harmonic signaland the digital, harmonic signal can have substantially similarfrequency and phase. Accordingly, the spectra of FIG. 4A are mixed witha DC component and a first-order analog harmonic signal.

Spectra 500 and 502 represent the spectra from mixing the spectra 400and 402 of FIG. 4A with the DC component. Spectrum 504 represents theresult of mixing the spectrum 400 with the first-order harmonic. Spectra506 and 508 represent the mixing of spectrum 402 of FIG. 4A with thefirst-order harmonic.

Similarly, FIG. 5B represents the spectra of the remixed signal for theinverted harmonic signal. Spectra 510 and 512 represent the mixing ofthe DC component with the spectra of FIG. 4B. Spectrum 514 representsthe mixing of the first-order harmonic of the inverted analog, harmonicsignal with the spectrum 410 of FIG. 4B. In particular, as thefirst-order harmonic of the inverted, analog harmonic signal has arelative 180 degree phase shift, the resulting spectrum 514 also has a180 degree phase shift, represented by the dashed line.

Spectrum 412 of FIG. 4B is also mixed with the first-order harmonic ofthe inverted, analog harmonic signal; however, the spectrum 412 alreadyhad a 180 degree induced phase shift. Thus, the additional 180 degreephase shift results in an effective 0 degree phase shift, represented bythe solid line of spectra 516 and 518.

FIG. 6 shows a spectrum 600 of the reconstructed digital input signalthat is output from the combiner shown in FIG. 1. Spectra 604 and 606represent the component sub-bands forming the spectrum 600. Spectrum 602represents an additional sideband from the mixing described with respectto FIGS. 5A and 5B. In this example, spectrum 602 is filtered out;however, in other examples sub-bands can extend beyond the first-orderharmonic frequency F₁. In this case, because spectrum 602 is generatedfrom a lower frequency sub-band it can be eliminated through destructivecombination.

Due to the relative phasing of the components of the remixed signals,sub-bands in their original frequency range combine constructively,while sub-bands outside of their original frequency range are phased tocombine destructively. Referring to FIGS. 5A, 5B, and 6, when combined,spectra 500 and 510 combine constructively, which results in spectrum604. Spectra 502 and 512 combine destructively as the spectra are out ofphase by 180 degrees. Thus, the spectrum that remains within thebaseband sub-band is the original sub-band.

Similarly, for the sub-band from approximately F₁/2 to F₁, spectra 506and 516 combine constructively into spectrum 606, while spectra 504 and514 combine destructively. Spectra 508 and 518 combine constructivelyinto spectrum 602; however, spectrum 602 can be filtered out as it isbeyond the expected input frequency range, which in this example isabout less than frequency F₁.

As illustrated by spectra 604 and 606, a transition occurs aroundfrequency F₁/2 that is the result of the filtering described above inreference to FIGS. 4A and 4B. The slopes of spectrum 604 and spectrum606 are complementary. Thus, when the frequency components of thespectrums 604 and 606 are combined, the resulting portion of thespectrum 600 substantially matches the original frequency spectrum.

Accordingly, by mixing the digital input signal with various harmonicsignals, sub-bands of the digital input signal are passed through thelower bandwidth of the DACs.

Although the mixed signals include overlapping sub-bands, because of thephasing of the harmonic signals, the sub-bands combine constructivelyand destructively when combined as described above to create asubstantially accurate analog reconstruction of the digital inputsignal.

In some examples, the analog and digital harmonic signals are frequencyand phase aligned with each other. One way to align the frequency andphase of the analog and harmonic signals is to choose a mixing frequencythat is a harmonic of a lower-speed clock that is present in the DACchannels in the analog domain, but is also correlated to the digitalharmonic signals. In other examples, a separate DAC channel serves as areference frequency that is multiplied with the mixing frequency of theanalog harmonic mixers. In some of the examples described above, theanalog harmonic mixers pass DC harmonic signals on all channels.Alternatively, the digital input signal can be split into bands, andeach band is multiplied with the appropriate mixing harmonic signal. Thedigital bands are then recombined before being converted to analogsignals. For each band, only one clock harmonic generates a mixingproduct within the low-pass filter bandwidth of the DAC channel. Theonly digital harmonic mixer that is required to handle a DC input is forthe low input band, which is mixed with the zero-th clock harmonic(i.e., multiplied by 1 or passed straight through without actuallyrequiring a mixer).

In another alternative, the analog mixers can pass DC harmonic signalson all channels by adapting a standard mixer topology to performharmonic mixing that includes the DC components.

FIGS. 7A and 7B illustrate examples of a harmonic mixer, which canrepresent any one or more of the harmonic mixers discussed above. FIG.7A illustrates a 2-way time-interleaving switch. FIG. 7B illustrates anN-way time-interleaving switch.

In these embodiments, switches 780 and/or 781 are configured to output asignal 782.

When using the 2-way switch 780, an input signal 784 or 786 is to output782 in response to a control signal 788. When using the N-way switch781, an input signal 784, 786, on through to the Nth input 787, isswitched to output 782, in response to the control signal 788. Forexample, the switch 781 can be a three-throw switch, a four-throwswitch, etc., up to an N-throw switch, which causes an input signal 784,786, on through to the Nth input 787 to spend 1/Nth of its time at theoutput 782. As further paths and sub-bands are added, the harmonics ofthe harmonic signals can be appropriately phased. In some embodiments,the relative phase shifts of the harmonic signals can be spaced in phaseby time shifts of one period divided by the number of sub-bands.

As the pulses get shorter compared to the overall clock cycle, theharmonic content gets richer. For instance, for a two-way or a three-wayswitch, the zero-order harmonic (DC) and the first-order harmonic areused. For a four-way or five-way switch, the zero-order harmonic, thefirst-order harmonic, and a second-order harmonic can be used. For asix-way or seven-way switch, the zero-order harmonic, the first-orderharmonic, a second-order harmonic, and a third-order harmonic can beused. As N increases, the pulses get narrower, thereby generating thericher harmonic content. The control signal 788 can be a signal having afundamental frequency of the first-order harmonic, or other suitableharmonic frequency, described above.

All bands of the input signals 784, 786, on through to the Nth input 787go through the output path 782.

For example, referring to switch 780, the control signal 788 can be asquare wave with a fundamental frequency of 20.3125 GHz. As a result ofthe switching, output 782 receives the input signal 784 or 786 duringone half-cycle of the control signal and receives the other input signalduring the opposite half-cycle. In effect, the output 782 is the inputsignal 784 or 786 multiplied by a square wave oscillating between zeroand one at 20.1325 GHz, for example. Such a square wave can berepresented by equation (4).

$\begin{matrix}{0.5 + {\frac{2}{\pi}{\sin \left( {2\pi \; F_{1}t} \right)}} + {\frac{2}{3\pi}{\sin \left( {6\pi \; F_{1}t} \right)}} + \ldots} & (4)\end{matrix}$

Equation (4) is the Taylor series expansion of such a square wave. TheDC and first two harmonics are listed. Here, F₁ is 20.1325 GHz. Althoughthe magnitudes of the components are different, equations (1) and (4)include similar harmonics.

Input 786 is similar to input 784; however, the time period over whichthe input signal 784 or 786 is routed to the output 782 is invertedrelative to input 784. The effect is again similar to multiplying theinput signal 784 or 786 with a square wave defined by equation (5).

$\begin{matrix}{0.5 - {\frac{2}{\pi}{\sin \left( {2\pi \; F_{1}t} \right)}} - {\frac{2}{3\pi}{\sin \left( {6\pi \; F_{1}t} \right)}} + \ldots} & (5)\end{matrix}$

Similar to equation (4), equation (5) is similar to the harmonic signaldescribed in equation (2) above. Thus, the multiplication effect of theswitching of the switch 780 is substantially similar to the mixing of asplit signal with the harmonic signal described above. In addition, inthis example, the switch acts as both the combiner and harmonic mixers.However, in other embodiments, the switch 780 could be a single polesingle throw switch and act as a single harmonic mixer.

Although the relative magnitudes of the DC component and the first-orderharmonic are different, such imbalance can be corrected through acompensation filter in the appropriate path. For example, the sub-banddescribed above between frequency F_(1/2) and frequency F₁ can have adifferent gain applied during recombination in the combiner than abaseband sub-band.

In addition, equations (4) and (5) above also list third-orderharmonics. In some embodiments, the third-order harmonics may bedesired. However, if not, the effect of such harmonics can becompensated with appropriate filtering. For example, the input signalscan be filtered to remove frequency components above frequency F₁. Thus,such frequency components would not be present to mix with a frequencyat 3*F₁. Moreover, filtering before a DAC can remove any higher orderfrequency components that may otherwise affect the analog signal due toaliasing.

In the event of interleaving errors due to mismatch, hardwareadjustments can be made for mixing clock amplitude and phase. Theadjustments can then be calibrated to minimize interleave mismatchspurs. Alternatively, or in addition to the above approach, hardwaremismatches can be characterized, and a linear, time-varying correctionfilter can be used to cancel the interleave spurs.

Further, in some cases, the switches might not always operate perfectly.For example, an errant switch might spend more time in one directionthan the other, thereby causing a skewed duty cycle. The digitalharmonic mixers can be configured to compensate for phase or amplitudeerrors that may be present in the analog harmonic signals by makingsubtle adjustments to the amplitude or phase of the analog harmonicsignals.

FIG. 8 is an example of another harmonic mixer. A switching circuit 800is configured to switch two input signals 808 and 810 alternatively tooutputs 802 and 804 in response to the control signal 806. The controlsignal 806 can again be a square wave or other similar signal to enablethe switches of the switching circuit 800 to switch. During onehalf-cycle of the control signal 806, input signal 808 is switched tooutput 802 while input signal 810 is switched to output 804. During theother half-cycle, the input signal 808 is switched to output 804 whileinput signal 810 is switched to output 802.

In some embodiments, the input signal 810 can be an inverted and scaledversion of the input signal 808. The result of such inputs and theswitching described above is a rebalancing of the DC and other harmonicsfrom the levels described above with respect to the switch 780 of FIG.7A. For example, input signal 810 can be a fractional inverted versionof the inputs signal 808. Instead of switching between 1 and 0 with theswitch 880 of FIG. 7A, the effective output of outputs 802 and 804 canbe switching between 1 and (2−π)/(2+π), for example. Thus, the amplitudeand DC level can be adjusted as desired to create the desired balancebetween the harmonics.

FIG. 9 illustrates an alternative example of a harmonic mixer. Theharmonic mixer 970 includes a splitter 972, a mixer 975, and a combiner977. The splitter 972 is configured to split an input signal 971 intosignals 973 and 974. Signal 974 is input to the combiner 977. As signal974 is not mixed with another signal, signal 974 acts as the DCcomponent of a harmonic mixer described above.

Signal 973 is input to the mixer 975. A signal 976 is mixed with thesignal 973. In some embodiments, signal 976 can be a single harmonic,such as the frequency F₁ described above. If additional harmonics aredesired, additional mixers can be provided and the respective outputscombined in combiner 977.

In another embodiment, the signal 976 can include multiple harmonics. Aslong as the bandwidth of the ports of the mixer 975 accommodate thedesired frequency ranges, a single mixer 975 can be used. However, sincethe DC component of the harmonic signals described above is passed tothe combiner 977 by a different path, the ports of the mixer receivingsignals 973 and 976 need not operate to DC. Accordingly, a wider varietyof mixers may be used. Once the signals 979 and 974 are combined in thecombiner 977, the output signal 978 can be substantially similar to amixed signal described above.

In some embodiments, the splitter 972 can, but need not, split the inputsignal 971 symmetrically. For example, a side of the splitter thatoutputs signal 974 has a bandwidth that is at or above the filteringcutoff frequency described above. A side of the splitter 972 thatoutputs signal 973 has a frequency range centered on a harmonic of thesignal 976 and a bandwidth of twice or greater of the filtering cutofffrequency described above. In other words, the frequency response of thesplitter 972 need not be equal for each path and can be tailored asdesired.

For example, FIG. 10 is a circuit diagram of an example mixer topology1000 that performs harmonic mixing with DC components by adapting adiode-ring mixer to implement the analog harmonic mixers for a two-wayinterleaved system. In this example, a harmonic signal 1002, such as amixer clock, can be input to a diode ring 1004 through transformer 1006.The input signals 1008, 1010 can be applied to inputs 1012 and 1014.Accordingly, depending on the harmonic signal, the input signals can bealternately switched to the output 1016, the center tap of thetransformer 1006. For example, the harmonic signal causes the rightdiodes to turn on when the bottom of the transformer is positive and thetop is negative, or the left diodes to turn on when the polarity of thetransformer is reversed. In this manner, the two input signals 1008,1010 are alternately routed to the output on opposite halves of theharmonic cycle. Note that in this example, the diode-ring mixer providesthe combined function of two mixers and the combiner.

In some embodiments, two paths and two overlapping sub-bands areimplemented. However, as mentioned above, any number of paths andsub-bands can be used. In such embodiments, the number of harmonics usedcan be equal to one plus one half of a number of sub-bands, roundeddown, where DC is included as a zero-order harmonic. For example, forthree sub-bands, only two harmonics can be used. Using the abovefrequency ranges as an example, the first-order harmonic can frequencyshift frequencies higher than frequency F₁ to the baseband sub-band. Thefirst-order harmonics of the harmonic signals can be phased with 120degree relative phase shifts.

Accordingly, when a sub-band is in the proper frequency range duringcombination in the combiner 58, the sub-band spectra will have the samephase shift, such as a 0 degree relative phase shift. In contrast, thethree components of a sub-band in the incorrect frequency range wouldoffset in phase from one another by 120 degrees. The resulting spectrawould destructively combine to eliminate the incorrect sub-band. Asfurther paths and sub-bands are added, the harmonics of the harmonicsignals can be appropriately phased. In some embodiments, the relativephase shifts of the harmonic signals can be spaced in phase by timeshifts of one period divided by the number of sub-bands.

Moreover, although the digital filtering, mixing, and combining havebeen described as discrete operations, such operations can be combined,incorporated into other functions, or the like. In addition, as theabove discussion assumed ideal components, additional compensation, canbe introduced into such processing as appropriate to correct fornon-ideal components.

Another embodiment includes computer readable code embodied on acomputer readable medium that when executed, causes the computer toperform any of the above-described operations. As used here, a computeris any device that can execute code. Microprocessors, programmable logicdevices, multiprocessor systems, digital signal processors, personalcomputers, or the like are all examples of such a computer. In someembodiments, the computer readable medium can be a tangible computerreadable medium that is configured to store the computer readable codein a non-transitory manner.

It will be appreciated that variations of the above-disclosed systemsand methods for generating waveforms and other features and functions,or alternatives thereof, may be desirably combined into many otherdifferent systems, methods, or applications. Also various presentlyunforeseen or unanticipated alternatives, modifications, variations, orimprovements therein may be subsequently made by those skilled in theart.

What is claimed is:
 1. A waveform generator, comprising: a splitterstructured to receive a digital input signal having an input signalfrequency bandwidth and structured to split the digital input signalinto a plurality of split signals, each of the split signals having asplit signal frequency bandwidth that is substantially similar to theinput signal frequency bandwidth; a plurality of digital, harmonicmixers structured to digitally mix an associated one of the splitsignals with an associated digital harmonic signal to generate aplurality of digital mixed signals; a plurality of digital to analogconverters, each of the plurality of digital to analog convertersstructured to convert an associated digital mixed signal of theplurality of digital mixed signals to an analog signal, each of thedigital to analog converters having an effective sample rate that isdifferent from a first order harmonic signal of at least one of theassociated digital, harmonic mixers; a plurality of analog, harmonicmixers structured to mix an associated one of the analog signals with ananalog harmonic signal to generate a plurality of mixed, analog signals;and a combiner structured to combine the plurality of mixed, analogsignals into an output signal having an output signal bandwidth that isgreater than a bandwidth of at least one of the plurality of digital toanalog converters.
 2. The waveform generator of claim 1, wherein thefirst-order harmonic signal of the at least one of the associateddigital, harmonic mixers is not an integer multiple or sub-multiple ofthe effective sample rate of the at least one digital to analogconverters.
 3. The waveform generator of claim 1, wherein thefirst-order harmonic of the at least one harmonic signal associated withthe digital, harmonic mixers is between the effective sample rate of theat least one of the digital to analog converters and one half theeffective sample rate of the at least one of the digital to analogconverters.
 4. The waveform generator of claim 1, wherein the pluralityof digital mixed signals includes at least two sub-bands of the digital,input signal within a bandwidth of a single-sub-band.
 5. The waveformgenerator of claim 4, wherein the single sub-band is a basebandsub-band.
 6. The waveform generator of claim 4, wherein each digitalmixed signal includes each sub-band of the digital input signal withinthe bandwidth of the single sub-band.
 7. The waveform generator of claim1, further comprising a plurality of symmetric, digital filters that arestructured to symmetrically filter the plurality of digital, mixedsignals before the digital, mixed signals are converted to analogsignals.
 8. The waveform generator of claim 1, wherein the analog,harmonic mixers have a first order harmonic that is different from theeffective sample rate of the digital to analog converters.
 9. Thewaveform generator of claim 3, wherein the first order harmonic of thedigital, harmonic mixer is substantially similar to the first orderharmonic of the analog, harmonic mixer.
 10. A method of generating awaveform, comprising: splitting a digital input signal having an inputsignal frequency bandwidth into a plurality of split signals, each ofthe split signals having a split signal frequency bandwidth that issubstantially similar to the input signal frequency bandwidth; digitallymixing each of the split signals with an associated digital harmonicsignal at an effective sample rate to generate a plurality of digitalmixed signals; converting the plurality of digital mixed signals to aplurality of analog signals at an effective sample rate that isdifferent from a first order harmonic signal of at least one of theassociated digital, harmonic mixing; mixing each of the analog signalswith an associated analog harmonic signal to generate a plurality ofmixed, analog signals; and combining the plurality of mixed, analogsignals into an output signal having an output signal bandwidth that isgreater than a bandwidth of at least one of the plurality of digital toanalog converters.
 11. The method of claim 9, wherein the first-orderharmonic signal is not an integer multiple or sub-multiple of aneffective conversion sample rate at which the plurality of digital,mixed signals are converted to the plurality of analog signals.
 12. Themethod of claim 9, wherein the first-order harmonic signal is between aneffective conversion sample rate at which the plurality of digital,mixed signals are converted to the plurality of analog signals and onehalf the effective conversion sample rate.
 13. The method of claim 9,wherein the plurality of digital, mixed signals includes at least twosub-bands of the digital, input signal within a bandwidth of a singlesub-band.
 14. The method of claim 12, wherein the single sub-band is abaseband sub-band.
 15. The method of claim 12, wherein each digital,mixed signal includes each sub-band of the digital input signal withinthe bandwidth of the single sub-band.
 16. The method of claim 12,wherein the first order harmonic of the digital, harmonic signal issubstantially similar to the first order harmonic of the analog,harmonic signal.
 17. The method of claim 12, further comprisingsymmetrically filtering the digital mixed signals before the digitalmixed signals are converted to analog signals.